Set theory is foundational to mathematics and, when sets are finite, to reasoning about the world. An intelligent system should perform set operations consistently, regardless of superficial variations in the operands. Initially designed for semantically-oriented NLP tasks, large language models (LLMs) are now being evaluated on algorithmic tasks. Because sets are comprised of arbitrary symbols (e.g. numbers, words), they provide an opportunity to test, systematically, the invariance of LLMs' algorithmic abilities under simple lexical or semantic variations. To this end, we present the SetLexSem Challenge, a synthetic benchmark that evaluates the performance of LLMs on set operations. SetLexSem assesses the robustness of LLMs' instruction-following abilities under various conditions, focusing on the set operations and the nature and construction of the set members. Evaluating seven LLMs with SetLexSem, we find that they exhibit poor robustness to variation in both operation and operands. We show -- via the framework's systematic sampling of set members along lexical and semantic dimensions -- that LLMs are not only not robust to variation along these dimensions but demonstrate unique failure modes in particular, easy-to-create semantic groupings of "deceptive" sets. We find that rigorously measuring language model robustness to variation in frequency and length is challenging and present an analysis that measures them independently. The code for reproducing the results of this paper, and for generating the SetLexSem Challenge dataset, is available at \href{https://github.com/amazon-science/SetLexSem-Challenge}{https://github.com/amazon-science/SetLexSem-Challenge}.

翻译：集合论是数学的基础，当集合为有限集时，也是理解世界的基础。一个智能系统应能一致地执行集合运算，而不受操作数表面变化的影响。最初为面向语义的自然语言处理任务设计的大型语言模型，现已在算法任务上进行评估。由于集合由任意符号（如数字、词语）构成，它们为系统性地测试LLMs在简单词汇或语义变化下算法能力的不变性提供了机会。为此，我们提出了SetLexSem挑战，这是一个评估LLMs在集合运算上性能的合成基准。SetLexSem评估LLMs在各种条件下遵循指令能力的鲁棒性，重点关注集合运算以及集合成员的性质与构造。通过SetLexSem评估七个LLMs，我们发现它们对运算和操作数的变化均表现出较差的鲁棒性。我们通过该框架沿词汇和语义维度对集合成员进行系统采样表明，LLMs不仅对这些维度的变化缺乏鲁棒性，而且在特定、易于创建的"欺骗性"集合语义分组中表现出独特的失败模式。我们发现，严格衡量语言模型对频率和长度变化的鲁棒性具有挑战性，并提出了一种独立测量它们的分析。用于复现本文结果及生成SetLexSem挑战数据集的代码可在\href{https://github.com/amazon-science/SetLexSem-Challenge}{https://github.com/amazon-science/SetLexSem-Challenge}获取。